class TestBetaMethods(geomstats.tests.TestCase):
def setUp(self):
warnings.simplefilter('ignore', category=UserWarning)
self.beta = BetaDistributions()
self.metric = BetaMetric()
self.n_samples = 10
self.dimension = self.beta.dimension
@geomstats.tests.np_and_pytorch_only
def test_random_uniform_and_belongs(self):
"""
Test that the random uniform method samples
on the beta distribution space.
"""
n_samples = self.n_samples
point = self.beta.random_uniform(n_samples)
result = self.beta.belongs(point)
expected = gs.array([True] * n_samples)
self.assertAllClose(expected, result)
@geomstats.tests.np_and_pytorch_only
def test_random_uniform(self):
"""
Test that the random uniform method samples points of the right shape
"""
point = self.beta.random_uniform(self.n_samples)
self.assertAllClose(gs.shape(point), (self.n_samples, self.dimension))
@geomstats.tests.np_only
def test_sample(self):
"""
Test that the sample method samples variates from beta distributions
with the specified parameters, using the law of large numbers
"""
n_samples = self.n_samples
tol = (n_samples * 10)**(-0.5)
point = self.beta.random_uniform(n_samples)
samples = self.beta.sample(point, n_samples * 10)
result = gs.mean(samples, axis=1)
expected = point[:, 0] / gs.sum(point, axis=1)
self.assertAllClose(result, expected, rtol=tol, atol=tol)
@geomstats.tests.np_only
def test_maximum_likelihood_fit(self):
"""
Test that the maximum likelihood fit method recovers
parameters of beta distribution.
"""
n_samples = self.n_samples
point = self.beta.random_uniform(n_samples)
samples = self.beta.sample(point, n_samples * 10)
fits = self.beta.maximum_likelihood_fit(samples)
expected = self.beta.belongs(fits)
result = gs.array([True] * n_samples)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_exp(self):
gs.random.seed(123)
n_samples = self.n_samples
points = self.beta.random_uniform(n_samples)
vectors = self.beta.random_uniform(n_samples)
initial_vectors = gs.array([[vec_x, vec_x] for vec_x in vectors[:, 0]])
points = gs.array([[param_a, param_a] for param_a in points[:, 0]])
result_points = self.metric.exp(initial_vectors, points)
result = gs.isclose(result_points[:, 0], result_points[:, 1]).all()
expected = gs.array([True] * n_samples)
self.assertAllClose(expected, result)
@geomstats.tests.np_only
def test_log_and_exp(self):
"""
Test that the Riemannian exponential
and the Riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
n_samples = self.n_samples
gs.random.seed(123)
base_point = self.beta.random_uniform(n_samples=n_samples, bound=5)
point = self.beta.random_uniform(n_samples=n_samples, bound=5)
log = self.metric.log(point, base_point, n_steps=500)
expected = point
result = self.metric.exp(tangent_vec=log, base_point=base_point)
self.assertAllClose(result, expected, rtol=1e-2)
def test_christoffels_vectorization(self):
"""
Check vectorization of Christoffel symbols in
spherical coordinates on the 2-sphere.
"""
points = self.beta.random_uniform(self.n_samples)
christoffel = self.metric.christoffels(points)
result = christoffel.shape
expected = gs.array(
[self.n_samples, self.dimension, self.dimension, self.dimension])
self.assertAllClose(result, expected)
class TestBetaDistributions(geomstats.tests.TestCase):
def setUp(self):
warnings.simplefilter('ignore', category=UserWarning)
self.beta = BetaDistributions()
self.metric = BetaMetric()
self.n_samples = 10
self.dim = self.beta.dim
def test_random_uniform_and_belongs(self):
"""Test random_uniform and belongs.
Test that the random uniform method samples
on the beta distribution space.
"""
point = self.beta.random_uniform()
result = self.beta.belongs(point)
expected = True
self.assertAllClose(expected, result)
def test_random_uniform_and_belongs_vectorization(self):
"""Test random_uniform and belongs.
Test that the random uniform method samples
on the beta distribution space.
"""
n_samples = self.n_samples
point = self.beta.random_uniform(n_samples)
result = self.beta.belongs(point)
expected = gs.array([True] * n_samples)
self.assertAllClose(expected, result)
def test_random_uniform(self):
"""Test random_uniform.
Test that the random uniform method samples points of the right shape
"""
point = self.beta.random_uniform(self.n_samples)
self.assertAllClose(gs.shape(point), (self.n_samples, self.dim))
def test_sample(self):
"""Test samples.
Test that the sample method samples variates from beta distributions
with the specified parameters, using the law of large numbers
"""
n_samples = self.n_samples
tol = (n_samples * 10)**(-0.5)
point = self.beta.random_uniform(n_samples)
samples = self.beta.sample(point, n_samples * 10)
result = gs.mean(samples, axis=1)
expected = point[:, 0] / gs.sum(point, axis=1)
self.assertAllClose(result, expected, rtol=tol, atol=tol)
def test_maximum_likelihood_fit(self):
"""Test maximum likelihood.
Test that the maximum likelihood fit method recovers
parameters of beta distribution.
"""
n_samples = self.n_samples
point = self.beta.random_uniform(n_samples)
samples = self.beta.sample(point, n_samples * 10)
fits = self.beta.maximum_likelihood_fit(samples)
expected = self.beta.belongs(fits)
result = gs.array([True] * n_samples)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_exp(self):
"""Test Exp.
Test that the Riemannian exponential at points on the first
bisector computed in the direction of the first bisector stays
on the first bisector.
"""
gs.random.seed(123)
n_samples = self.n_samples
points = self.beta.random_uniform(n_samples)
vectors = self.beta.random_uniform(n_samples)
initial_vectors = gs.array([[vec_x, vec_x] for vec_x in vectors[:, 0]])
points = gs.array([[param_a, param_a] for param_a in points[:, 0]])
result_points = self.metric.exp(initial_vectors, points)
result = gs.isclose(result_points[:, 0], result_points[:, 1]).all()
expected = gs.array([True] * n_samples)
self.assertAllClose(expected, result)
@geomstats.tests.np_only
def test_log_and_exp(self):
"""Test Log and Exp.
Test that the Riemannian exponential
and the Riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
n_samples = self.n_samples
gs.random.seed(123)
base_point = self.beta.random_uniform(n_samples=n_samples, bound=5)
point = self.beta.random_uniform(n_samples=n_samples, bound=5)
log = self.metric.log(point, base_point, n_steps=500)
expected = point
result = self.metric.exp(tangent_vec=log, base_point=base_point)
self.assertAllClose(result, expected, rtol=1e-2)
@geomstats.tests.np_only
def test_exp_vectorization(self):
"""Test vectorization of Exp.
Test the case with one initial point and several tangent vectors.
"""
point = self.beta.random_uniform()
tangent_vec = gs.array([1., 2.])
n_tangent_vecs = 10
t = gs.linspace(0., 1., n_tangent_vecs)
tangent_vecs = gs.einsum('i,...k->...ik', t, tangent_vec)
end_points = self.metric.exp(tangent_vec=tangent_vecs,
base_point=point)
result = end_points.shape
expected = (n_tangent_vecs, 2)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_log_vectorization(self):
"""Test vectorization of Log.
Test the case with several base points and one end point.
"""
n_points = 10
base_points = self.beta.random_uniform(n_samples=n_points)
point = self.beta.random_uniform()
tangent_vecs = self.metric.log(base_point=base_points, point=point)
result = tangent_vecs.shape
expected = (n_points, 2)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_christoffels_vectorization(self):
"""Test Christoffel synbols.
Check vectorization of Christoffel symbols.
"""
points = self.beta.random_uniform(self.n_samples)
christoffel = self.metric.christoffels(points)
result = christoffel.shape
expected = gs.array([self.n_samples, self.dim, self.dim, self.dim])
self.assertAllClose(result, expected)
def test_metric_matrix(self):
point = gs.array([1., 1.])
result = self.beta.metric.metric_matrix(point)
expected = gs.array([[1., -0.644934066], [-0.644934066, 1.]])
self.assertAllClose(result, expected)
self.assertRaises(ValueError, self.beta.metric.metric_matrix)
def test_point_to_pdf(self):
"""Test point_to_pdf.
Check vectorization of the computation of the pdf.
"""
point = self.beta.random_uniform(n_samples=2)
pdf = self.beta.point_to_pdf(point)
x = gs.linspace(0., 1., 10)
result = pdf(x)
pdf1 = beta.pdf(x, a=point[0, 0], b=point[0, 1])
pdf2 = beta.pdf(x, a=point[1, 0], b=point[1, 1])
expected = gs.stack([gs.array(pdf1), gs.array(pdf2)], axis=1)
self.assertAllClose(result, expected)